1 Introduction

This document is devoted to depict all the results obtained after the different simulations of the paper Martinez-Minaya et al., 2021.

2 Simulation: Scenario 1

This simula

3 Simulation: Scenario 2

4 Simulation: Scenario 3

4.1 Data simulation

To conduct the tests, we have simulated different datasets with the following structures. Each dataset has 4 covariates, one per category and a shared random effect. \[\begin{eqnarray} \log(\alpha_{1n}) & = & \eta_{1n} = \beta_{1}^1 \cdot v_{1n} + w^1(j_n) \,, \nonumber \\ \log(\alpha_{2n}) & = & \eta_{2n} = \beta_{1}^2 \cdot v_{2n} + w^1(j_n) \,, \nonumber \\ \log(\alpha_{3n}) & = & \eta_{3n} = \beta_{1}^3 \cdot v_{3n} + w^2(j_n) \,, \nonumber \\ \log(\alpha_{4n}) & = & \eta_{4n} = \beta_{1}^4 \cdot v_{4n} + w^2(j_n) \,, \nonumber \\ \end{eqnarray}\] where \(v_{kn}\) are covariates \(k = 1, \ldots, 4\) simulated from a random uniform (-1, 1), and \(w^1(j_n)\) and \(w^2(j_n)\) are iid shared random effects. \(j_n = 1, \ldots, J\), being \(J\) the levels of the factor.

We simulate datasets with N= 50, 100 and 500; and with different sizes for J. We have fitted the models using Gaussian priors for \(\beta\)s, Half Normal and pc-priors for \(\sigma_1\) and \(\sigma_2\). We are going to fit four different models:

  1. Short-JAGS with Half Normal for standard deviations (mean = 0, sd = 1).

  2. dirinla with pc-priors for standard deviations (sigma = 10, alpha = 0.01).

  3. Long-JAGS with Half Normal for standard deviations (mean = 0, sd = 1).

  4. dirinla with Half Normal for standard deviations (mean = 0, sd = 1).

In order to check the results, we have computed:

  • Posterior distributions and have compared it.

  • Computational times

  • Mean and sd of the fixed effects

  • Two measures: \(ratio_1\) (closer 0, better is the dirinla fit) and \(ratio_2\) (closer 1, better is the dirinla fit), computed for the parameters and hyperparameters: \[\begin{eqnarray}\label{eq:ratio1_ratio2} ratio_1 & = & (E(\phi_{dirinla}) - E(\phi_{long R-JAGS}))/ SD(\phi_{long R-JAGS}) \,\,, \\ ratio_2 & = & SD(\phi_{dirinla})/ SD(\phi_{long R-JAGS}) \,\,, \end{eqnarray}\]

  • \(n.eff\) and \(Rhat\) for short and long JAGS.

4.2 Results

summary_print <- function(N, J)
{
  cat("\n")
  cat(sprintf(paste0("#### J = ", J, "\n")))
  cat("**Parameters** \n")
  cat(paste0("![](IMG/examples_simulation4_slopes_", N, "_", J, "/examples_simulation4_slopes_", N, "_", J, "-1.png){width=100%}"))

  cat("**Hyperparameters** \n ")
  cat(paste0("![](IMG/examples_simulation4_sigma_", N, "_", J, "/examples_simulation4_sigma_", N, "_", J, "-1.png){width=100%} \n \n "))
  cat("<br>")
  if(N<=500)
  {
      a <- readRDS("simulation4_50-500.RDS")
  }else{
      a <- readRDS("simulation4_1000.RDS")
  }
  a <- a[, c(paste0(N, "-", J))]
  
  #Half normal
  # names(a)[c(7,8, 11, 12)] <- c("ratio1_sigma_pc", "ratio2_sigma_pc", "ratio1_sigma_log_hn", "ratio2_sigma_log_hn")
  
  

    
  num <- length(a) - 1
  names_ele <- names(a)
  names(a[[1]]) <- c("JAGS", "dirinla pc", "LONG-JAGS", "dirinla hn")
  names(a[c(13,14)]) <- c("res_check_jags", "res_check_long_jags")
  for (i in 1:num){
    b <- a[i]
    if(i == 2)
    {
      result <- as.numeric(b[[1]]) %>% matrix(., nrow = 4)
      colnames(result) <- colnames(b[[1]])
      colnames(result) <- c("JAGS_mean", "JAGS_sd", "INLA_PC_mean", "INLA_PC_sd", "LONG_JAGS_mean", "LONG_JAGS_sd", "INLA_HN_mean", "INLA_HN_sd")  
      rownames(result) <- rownames(b[[1]])
      
      result %>%  knitr::kable(.,  digits = c(4)) %>% 
        print(.)
    }else{
     cat(paste0("**", names_ele[i], "** \n "))
     b[[1]] %>% as.matrix(.) %>% t(.) %>% knitr::kable(.,  digits = c(4)) %>% print(.)
     cat("\n \n ")
    }
  }
}

4.2.1 N = 50

summary_print(N = 50, J = 2)

4.2.1.1 J = 2

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
86.44 24.36 4253.34 17.89
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.5310 0.2567 -1.5414 0.2490 -1.5315 0.2583 -1.5415 0.2489
beta12 2.0258 0.2145 2.0424 0.2192 2.0254 0.2147 2.0425 0.2190
beta13 1.0751 0.2111 1.0982 0.1901 1.0766 0.2124 1.0988 0.1900
beta14 -2.9160 0.1876 -2.9481 0.1918 -2.9203 0.1869 -2.9490 0.1916

ratio1_beta1_pc

-0.0382 0.0795 0.1016 -0.1486

ratio1_beta1_hn

-0.0388 0.0798 0.1041 -0.1533

ratio2_beta1_pc

0.9246 1.0465 0.833 1.0529

ratio2_beta1_hn

0.9285 1.0509 0.8128 1.0532

ratio1_sigma_pc

sigma1 sigma2
0.0304 0.1802

ratio2_sigma_pc

sigma1 sigma2
1.2871 1.1437

ratio1_sigma_hn

sigma1 sigma2
0.0142 0.1565

ratio2_sigma_hn

sigma1 sigma2
1.2072 1.0707

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.0289 0.265

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.7877 0.5473

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.0373 0.2622

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.7318 0.5177

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001 1.0009 1.0009 1.0013 1.0009 1.0045 1.0015
n.eff 11000.000 11000.0000 11000.0000 5100.0000 11000.0000 5700.0000 3100.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001
n.eff 5.400e+05 3.900e+05 2.500e+05 5.400e+05 5.400e+05 2.100e+05 61000.000 
summary_print(N = 50, J = 5)

4.2.1.2 J = 5

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
84.7 23.86 4334.2 20.95
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.3347 0.2569 -1.3089 0.2479 -1.3354 0.2578 -1.3089 0.2478
beta12 1.8220 0.2103 1.8295 0.2188 1.8212 0.2109 1.8287 0.2187
beta13 0.9425 0.1937 0.9586 0.1866 0.9413 0.1922 0.9582 0.1866
beta14 -2.7211 0.2003 -2.7397 0.2008 -2.7212 0.2003 -2.7391 0.2008

ratio1_beta1_pc

0.103 0.0394 0.09 -0.0925

ratio1_beta1_hn

0.1027 0.0357 0.0877 -0.0898

ratio2_beta1_pc

0.9217 1.0824 0.976 1.0029

ratio2_beta1_hn

0.9233 1.0869 0.9576 1.0077

ratio1_sigma_pc

sigma1 sigma2
-0.1074 0.0819

ratio2_sigma_pc

sigma1 sigma2
0.9862 1.1708

ratio1_sigma_hn

sigma1 sigma2
-0.1145 -0.0011

ratio2_sigma_hn

sigma1 sigma2
0.9156 0.9643

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
-0.0769 0.0712

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.7606 1.0463

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
-0.0707 0.0064

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.7238 0.9531

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0009 1.0009 1.0009 1.0012 1.0015 1.0076 1.0009
n.eff 11000.0000 11000.0000 11000.0000 6600.0000 3100.0000 1700.0000 11000.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 4.400e+05 4.300e+05 1.200e+05 5.400e+05 5.400e+05 5.400e+05 3.800e+05 
summary_print(N = 50, J = 10)

4.2.1.3 J = 10

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
85.13 20.62 4228.33 21.36
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.4256 0.2390 -1.4354 0.2252 -1.4216 0.2416 -1.4361 0.2251
beta12 2.0345 0.2446 2.0971 0.2188 2.0308 0.2443 2.0976 0.2187
beta13 0.9472 0.1927 0.9651 0.1888 0.9475 0.1919 0.9651 0.1888
beta14 -2.4796 0.2092 -2.5756 0.1860 -2.4741 0.2113 -2.5755 0.1859

ratio1_beta1_pc

-0.0571 0.2712 0.0919 -0.4804

ratio1_beta1_hn

-0.06 0.2734 0.0917 -0.48

ratio2_beta1_pc

0.8642 0.806 1.0062 0.7746

ratio2_beta1_hn

0.8676 0.8095 0.9824 0.7762

ratio1_sigma_pc

sigma1 sigma2
0.0376 0.543

ratio2_sigma_pc

sigma1 sigma2
0.9205 0.8862

ratio1_sigma_hn

sigma1 sigma2
0.0071 0.541

ratio2_sigma_hn

sigma1 sigma2
0.8641 0.844

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.0603 0.5148

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.81 0.2177

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.0363 0.5179

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.7799 0.2086

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0013 1.0009 1.0009 1.0019 1.0009 1.0013 1.0408
n.eff 4600.0000 11000.0000 11000.0000 2000.0000 11000.0000 5000.0000 140.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 2.500e+05 5.200e+05 5.400e+05 5.400e+05 5.400e+05 3.400e+05 1.200e+05 
summary_print(N = 50, J = 25)

4.2.1.4 J = 25

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
85.43 24.51 4258.83 27.08
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.6670 0.2697 -1.7341 0.2513 -1.6678 0.2718 -1.7340 0.2512
beta12 1.8052 0.2592 1.8206 0.2346 1.8047 0.2589 1.8205 0.2346
beta13 0.7890 0.2320 0.8647 0.1921 0.7878 0.2313 0.8645 0.1921
beta14 -3.3133 0.2003 -3.3610 0.1944 -3.3130 0.2005 -3.3609 0.1944

ratio1_beta1_pc

-0.244 0.0613 0.3325 -0.2394

ratio1_beta1_hn

-0.2435 0.0609 0.3315 -0.2388

ratio2_beta1_pc

0.851 0.8254 0.7176 0.9397

ratio2_beta1_hn

0.8542 0.8296 0.7002 0.9416

ratio1_sigma_pc

sigma1 sigma2
0.2252 -0.5005

ratio2_sigma_pc

sigma1 sigma2
0.9417 1.1101

ratio1_sigma_hn

sigma1 sigma2
0.2159 -0.4983

ratio2_sigma_hn

sigma1 sigma2
0.913 1.086

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.2309 -0.58

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.5614 1.4537

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.2264 -0.5731

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.5486 1.4191

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0011 1.001 1.0009 1.001 1.0014 1.0021 1.0019
n.eff 8800.0000 11000.000 11000.0000 11000.000 3600.0000 2600.0000 11000.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.0025 1.001e+00
n.eff 5.400e+05 5.400e+05 5.400e+05 5.400e+05 1.600e+05 19000.0000 5.400e+05 
summary_print(N = 50, J = 50)

4.2.1.5 J = 50

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
90.12 27.47 4452.67 26.69
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.9463 0.2607 -2.0426 0.2377 -1.9464 0.2603 -2.0426 0.2377
beta12 1.9259 0.2747 1.8217 0.2324 1.9295 0.2749 1.8219 0.2324
beta13 1.2146 0.2079 1.1080 0.1906 1.2192 0.2071 1.1079 0.1906
beta14 -2.9008 0.1871 -2.9768 0.1912 -2.9048 0.1874 -2.9766 0.1912

ratio1_beta1_pc

-0.3694 -0.3921 -0.5369 -0.3842

ratio1_beta1_hn

-0.3693 -0.3914 -0.5373 -0.3834

ratio2_beta1_pc

0.8279 0.7178 0.8805 1.0416

ratio2_beta1_hn

0.8342 0.722 0.8595 1.0404

ratio1_sigma_pc

sigma1 sigma2
0.1322 0.1228

ratio2_sigma_pc

sigma1 sigma2
0.7792 0.7058

ratio1_sigma_hn

sigma1 sigma2
0.1243 0.1557

ratio2_sigma_hn

sigma1 sigma2
0.7624 0.6984

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.1718 0.256

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.4282 0.2914

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.1675 0.2815

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.4209 0.2743

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0012 1.001 1.0015 1.0013 1.0045 1.0063 1.1323
n.eff 6500.0000 11000.000 3000.0000 4200.0000 540.0000 8600.0000 58.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.0033 1.0013
n.eff 5.400e+05 5.400e+05 5.400e+05 5.400e+05 1.300e+05 18000.0000 7700.0000

4.2.2 N = 100

summary_print(N = 100, J = 2)

4.2.2.1 J = 2

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
182.01 16.52 8993.8 11.66
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.4677 0.1781 -1.4736 0.1785 -1.4648 0.1787 -1.4751 0.1785
beta12 1.8881 0.1324 1.8936 0.1427 1.8885 0.1334 1.8951 0.1426
beta13 1.1340 0.1761 1.1409 0.1739 1.1352 0.1762 1.1412 0.1738
beta14 -2.7319 0.1718 -2.7398 0.1789 -2.7313 0.1714 -2.7399 0.1788

ratio1_beta1_pc

-0.0487 0.0386 0.0322 -0.0496

ratio1_beta1_hn

-0.0576 0.0494 0.0339 -0.0502

ratio2_beta1_pc

0.9851 1.1534 1.0092 1.0859

ratio2_beta1_hn

0.9967 1.1581 0.9899 1.094

ratio1_sigma_pc

sigma1 sigma2
0.3601 0.4413

ratio2_sigma_pc

sigma1 sigma2
2.5098 2.9556

ratio1_sigma_hn

sigma1 sigma2
0.0087 -0.0305

ratio2_sigma_hn

sigma1 sigma2
1.1849 1.1101

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.232 0.2824

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
1.4307 1.4938

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
-0.0153 -0.0531

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
1.0868 1.0724

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001 1.001 1.0011 1.0011 1.0009 1.0009 1.0017
n.eff 11000.000 11000.000 7600.0000 7400.0000 11000.0000 11000.0000 2400.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 5.400e+05 5.400e+05 3.900e+05 1.400e+05 5.400e+05 4.800e+05 3.900e+05 
summary_print(N = 100, J = 5)

4.2.2.2 J = 5

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
178.59 18.83 8694.55 19.65
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.2893 0.1773 -1.2766 0.1717 -1.2869 0.1786 -1.2767 0.1716
beta12 2.0838 0.1264 2.0907 0.1327 2.0827 0.1266 2.0907 0.1327
beta13 0.9483 0.1519 0.9741 0.1549 0.9479 0.1528 0.9743 0.1549
beta14 -3.1886 0.1676 -3.1956 0.1537 -3.1885 0.1663 -3.1960 0.1537

ratio1_beta1_pc

0.0577 0.0627 0.1712 -0.043

ratio1_beta1_hn

0.0573 0.0629 0.1729 -0.0454

ratio2_beta1_pc

0.9132 1.1114 1.0648 0.8516

ratio2_beta1_hn

0.9188 1.1124 1.0469 0.8568

ratio1_sigma_pc

sigma1 sigma2
-0.0095 0.0769

ratio2_sigma_pc

sigma1 sigma2
1.0342 0.9118

ratio1_sigma_hn

sigma1 sigma2
-0.0619 0.0717

ratio2_sigma_hn

sigma1 sigma2
0.8992 0.8789

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
-0.0218 0.1221

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
1.0689 0.7147

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
-0.0639 0.122

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.9908 0.6975

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001 1.0012 1.0009 1.001 1.0011 1.001 1.0033
n.eff 11000.000 6100.0000 11000.0000 11000.000 7300.0000 11000.000 4600.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 5.400e+05 5.400e+05 5.400e+05 5.400e+05 4.100e+05 5.400e+05 3.000e+05 
summary_print(N = 100, J = 10)

4.2.2.3 J = 10

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
169.71 20.46 8523.84 20
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.7246 0.1731 -1.7354 0.1657 -1.7267 0.1739 -1.7352 0.1657
beta12 2.0154 0.1287 2.0169 0.1271 2.0127 0.1273 2.0170 0.1270
beta13 0.9611 0.1545 0.9841 0.1523 0.9611 0.1557 0.9839 0.1523
beta14 -3.0510 0.1638 -3.0667 0.1542 -3.0537 0.1640 -3.0664 0.1542

ratio1_beta1_pc

-0.0496 0.0327 0.1476 -0.0791

ratio1_beta1_hn

-0.0485 0.0334 0.1466 -0.0776

ratio2_beta1_pc

0.8974 1.0042 0.9922 0.882

ratio2_beta1_hn

0.908 1.0085 0.9732 0.889

ratio1_sigma_pc

sigma1 sigma2
0.079 0.0942

ratio2_sigma_pc

sigma1 sigma2
1.0579 0.993

ratio1_sigma_hn

sigma1 sigma2
-0.0072 0.0783

ratio2_sigma_hn

sigma1 sigma2
0.9312 0.949

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.0776 0.1056

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
1.0395 0.9101

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
-0.0022 0.0943

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.9683 0.8837

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0009 1.001 1.001 1.0013 1.0009 1.0009 1.0013
n.eff 11000.0000 11000.000 11000.000 4800.0000 11000.0000 11000.0000 5000.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 4.600e+05 5.400e+05 5.400e+05 5.400e+05 5.400e+05 5.400e+05 5.400e+05 
summary_print(N = 100, J = 25)

4.2.2.4 J = 25

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
171.42 21.07 8552.03 16.39
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.4289 0.1759 -1.4926 0.1636 -1.4268 0.1769 -1.4926 0.1636
beta12 2.0190 0.1362 2.0410 0.1262 2.0218 0.1354 2.0413 0.1262
beta13 1.0814 0.1606 1.1473 0.1533 1.0818 0.1605 1.1472 0.1533
beta14 -3.0197 0.1655 -3.0657 0.1471 -3.0195 0.1669 -3.0652 0.1471

ratio1_beta1_pc

-0.3719 0.1425 0.4081 -0.2773

ratio1_beta1_hn

-0.3717 0.1443 0.4075 -0.2737

ratio2_beta1_pc

0.8482 0.8739 0.9473 0.7757

ratio2_beta1_hn

0.8558 0.8792 0.9262 0.7798

ratio1_sigma_pc

sigma1 sigma2
0.1888 0.8524

ratio2_sigma_pc

sigma1 sigma2
1.0002 0.7479

ratio1_sigma_hn

sigma1 sigma2
0.1554 0.8476

ratio2_sigma_hn

sigma1 sigma2
0.9636 0.7346

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.1933 0.6323

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.9173 0.2027

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.163 0.6306

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.8966 0.1998

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001 1.0009 1.0009 1.0009 1.0013 1.001 1.0157
n.eff 11000.000 11000.0000 11000.0000 11000.0000 5100.0000 11000.000 580.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001 1.001e+00 1.0083
n.eff 2.000e+05 5.400e+05 3.600e+05 5.400e+05 73000.000 5.400e+05 4000.0000 
summary_print(N = 100, J = 100)

4.2.2.5 J = 100

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
178.87 23.08 9050.28 23.94
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.7892 0.1922 -1.7381 0.1640 -1.7896 0.1929 -1.7383 0.1640
beta12 2.2428 0.1538 2.2201 0.1394 2.2419 0.1542 2.2206 0.1393
beta13 1.1452 0.1699 1.0795 0.1566 1.1456 0.1678 1.0788 0.1566
beta14 -3.0647 0.1783 -3.1410 0.1583 -3.0678 0.1769 -3.1401 0.1584

ratio1_beta1_pc

0.267 -0.1416 -0.3943 -0.4137

ratio1_beta1_hn

0.266 -0.1386 -0.3983 -0.4086

ratio2_beta1_pc

0.72 0.8248 0.9083 0.8039

ratio2_beta1_hn

0.7199 0.8275 0.8803 0.8013

ratio1_sigma_pc

sigma1 sigma2
0.4395 0.2891

ratio2_sigma_pc

sigma1 sigma2
0.6985 0.5968

ratio1_sigma_hn

sigma1 sigma2
0.4262 0.2969

ratio2_sigma_hn

sigma1 sigma2
0.6889 0.5892

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.4385 0.3258

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.5128 0.2043

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.4277 0.3313

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.5082 0.2006

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0016 1.0014 1.0029 1.001 1.0038 1.0016 1.0166
n.eff 2600.0000 4000.0000 970.0000 11000.000 670.0000 2800.0000 160.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001 1.001e+00 1.001 1.001e+00 1.0012
n.eff 5.400e+05 5.400e+05 73000.000 5.400e+05 61000.000 3.400e+05 11000.0000

4.2.3 N = 500

summary_print(N = 500, J = 2)

4.2.3.1 J = 2

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
857.67 22.91 43141.23 16.48
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.4931 0.0622 -1.4950 0.0649 -1.4934 0.0623 -1.4948 0.0649
beta12 2.0117 0.0611 2.0134 0.0597 2.0116 0.0611 2.0131 0.0597
beta13 1.0572 0.0566 1.0593 0.0576 1.0581 0.0569 1.0593 0.0576
beta14 -3.0679 0.0557 -3.0696 0.0555 -3.0680 0.0563 -3.0696 0.0555

ratio1_beta1_pc

-0.0246 0.0301 0.0205 -0.0277

ratio1_beta1_hn

-0.0216 0.0255 0.021 -0.028

ratio2_beta1_pc

1.0802 0.9736 1.0439 0.98

ratio2_beta1_hn

1.0894 0.9838 1.0204 0.9751

ratio1_sigma_pc

sigma1 sigma2
0.9784 0.6641

ratio2_sigma_pc

sigma1 sigma2
4.6735 3.6745

ratio1_sigma_hn

sigma1 sigma2
0.0533 0.0854

ratio2_sigma_hn

sigma1 sigma2
1.1097 1.1906

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.6877 0.4716

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
1.7296 1.4915

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.0522 0.0868

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
1.0059 0.9952

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0011 1.001 1.001 1.0009 1.001 1.0016 1.0013
n.eff 8700.0000 11000.000 11000.000 11000.0000 11000.000 2700.0000 4700.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 4.800e+05 5.400e+05 3.400e+05 4.900e+05 5.400e+05 5.400e+05 2.300e+05 
summary_print(N = 500, J = 5)

4.2.3.2 J = 5

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
895.82 26.27 44329.66 24.28
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.4669 0.0624 -1.4687 0.0626 -1.4674 0.0618 -1.4687 0.0626
beta12 1.9733 0.0576 1.9753 0.0568 1.9742 0.0581 1.9753 0.0568
beta13 0.9054 0.0614 0.9071 0.0639 0.9057 0.0620 0.9071 0.0639
beta14 -2.9685 0.0599 -2.9706 0.0588 -2.9693 0.0592 -2.9705 0.0588

ratio1_beta1_pc

-0.0206 0.0189 0.0226 -0.0211

ratio1_beta1_hn

-0.0211 0.0197 0.0222 -0.0194

ratio2_beta1_pc

1.0194 0.9675 1.0809 0.9859

ratio2_beta1_hn

1.0309 0.9902 1.0637 0.9901

ratio1_sigma_pc

sigma1 sigma2
0.2251 -0.0265

ratio2_sigma_pc

sigma1 sigma2
1.3176 0.7906

ratio1_sigma_hn

sigma1 sigma2
0.0287 -0.0144

ratio2_sigma_hn

sigma1 sigma2
0.9427 0.7998

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.2123 -0.0064

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
1.1331 0.9152

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.0393 0.0076

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.9575 0.9155

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0011 1.001 1.0009 1.001 1.0009 1.0009 1.0009
n.eff 7300.0000 11000.000 11000.0000 11000.000 11000.0000 11000.0000 11000.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001 1.001e+00
n.eff 5.100e+05 5.400e+05 5.400e+05 4.100e+05 5.400e+05 93000.000 3.100e+05 
summary_print(N = 500, J = 10)

4.2.3.3 J = 10

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
859.89 27.76 43231.97 24.61
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.5244 0.0609 -1.5291 0.0614 -1.5246 0.0614 -1.5291 0.0614
beta12 2.0027 0.0570 2.0042 0.0574 2.0028 0.0570 2.0043 0.0574
beta13 0.9601 0.0632 0.9613 0.0629 0.9596 0.0634 0.9613 0.0629
beta14 -3.0030 0.0575 -3.0072 0.0577 -3.0035 0.0577 -3.0072 0.0577

ratio1_beta1_pc

-0.0738 0.0245 0.027 -0.0642

ratio1_beta1_hn

-0.0743 0.025 0.0268 -0.0633

ratio2_beta1_pc

0.9969 1.0323 1.0038 1.0101

ratio2_beta1_hn

1.0069 1.0457 0.9799 1.0075

ratio1_sigma_pc

sigma1 sigma2
0.0534 -0.0205

ratio2_sigma_pc

sigma1 sigma2
0.9511 0.8939

ratio1_sigma_hn

sigma1 sigma2
0.013 -0.0113

ratio2_sigma_hn

sigma1 sigma2
0.893 0.8955

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.0615 -0.0136

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.9726 0.9556

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.0234 -0.0033

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.9374 0.9526

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0016 1.0011 1.001 1.001 1.001 1.0009 1.0009
n.eff 2500.0000 8800.0000 11000.000 11000.000 11000.000 11000.0000 11000.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 5.400e+05 5.400e+05 2.300e+05 5.400e+05 5.400e+05 4.500e+05 5.400e+05 
summary_print(N = 500, J = 25)

4.2.3.4 J = 25

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
861.24 24.5 43212.64 22.48
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.5330 0.0655 -1.5410 0.0636 -1.5340 0.0654 -1.5410 0.0636
beta12 2.0678 0.0599 2.0721 0.0578 2.0672 0.0596 2.0721 0.0578
beta13 1.0241 0.0625 1.0294 0.0616 1.0242 0.0626 1.0294 0.0616
beta14 -3.0033 0.0621 -3.0137 0.0583 -3.0044 0.0617 -3.0137 0.0583

ratio1_beta1_pc

-0.107 0.0808 0.0835 -0.15

ratio1_beta1_hn

-0.1071 0.0811 0.0835 -0.1498

ratio2_beta1_pc

0.9402 0.9586 0.9846 0.9014

ratio2_beta1_hn

0.9513 0.9736 0.9605 0.8968

ratio1_sigma_pc

sigma1 sigma2
0.029 0.0559

ratio2_sigma_pc

sigma1 sigma2
0.9632 0.9682

ratio1_sigma_hn

sigma1 sigma2
0.0184 0.0596

ratio2_sigma_hn

sigma1 sigma2
0.9482 0.9666

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.0322 0.0603

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.973 0.9628

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.0223 0.0642

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.9618 0.9599

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001 1.001 1.0009 1.0009 1.0012 1.001 1.001
n.eff 11000.000 11000.000 11000.0000 11000.0000 6700.0000 11000.000 11000.000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 3.700e+05 5.400e+05 5.400e+05 5.400e+05 5.400e+05 2.000e+05 5.400e+05 
summary_print(N = 500, J = 500)

4.2.3.5 J = 500

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
918.89 27.8 46139.69 28.42
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.3821 0.0727 -1.4206 0.0655 -1.3825 0.0725 -1.4206 0.0655
beta12 2.0684 0.0657 2.1061 0.0610 2.0676 0.0655 2.1062 0.0610
beta13 1.1385 0.0673 1.1908 0.0621 1.1382 0.0669 1.1907 0.0621
beta14 -2.9930 0.0659 -3.0641 0.0601 -2.9924 0.0647 -3.0640 0.0601

ratio1_beta1_pc

-0.5255 0.5879 0.7854 -1.1078

ratio1_beta1_hn

-0.5261 0.589 0.7848 -1.107

ratio2_beta1_pc

0.8076 0.8833 0.862 0.8466

ratio2_beta1_hn

0.8221 0.9023 0.8802 0.8727

ratio1_sigma_pc

sigma1 sigma2
0.8772 0.9221

ratio2_sigma_pc

sigma1 sigma2
0.7798 0.6977

ratio1_sigma_hn

sigma1 sigma2
0.8729 0.9265

ratio2_sigma_hn

sigma1 sigma2
0.7774 0.6959

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.8458 0.8105

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.6344 0.4132

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.842 0.8141

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.633 0.4116

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0013 1.0011 1.001 1.001 1.0019 1.0022 1.0135
n.eff 5100.0000 7300.0000 11000.000 11000.000 1900.0000 1500.0000 170.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001
n.eff 5.400e+05 5.400e+05 5.400e+05 3.700e+05 1.100e+05 1.800e+05 39000.000

4.2.4 N = 1000

summary_print(N = 1000, J = 2)

4.2.4.1 J = 2

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
1922.16 42.31 92315.65 32.39
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.5430 0.0433 -1.5443 0.0446 -1.5437 0.0432 -1.5443 0.0446
beta12 2.0529 0.0422 2.0535 0.0421 2.0523 0.0422 2.0536 0.0421
beta13 1.0588 0.0458 1.0592 0.0461 1.0585 0.0459 1.0592 0.0461
beta14 -3.0300 0.0417 -3.0305 0.0423 -3.0298 0.0419 -3.0305 0.0423

ratio1_beta1_pc

-0.014 0.0299 0.0143 -0.0186

ratio1_beta1_hn

-0.0143 0.0301 0.0142 -0.0184

ratio2_beta1_pc

1.075 1.0351 1.011 1.0286

ratio2_beta1_hn

1.0819 1.0062 1.0042 0.995

ratio1_sigma_pc

sigma1 sigma2
-0.0166 -0.1335

ratio2_sigma_pc

sigma1 sigma2
1.0868 0.7449

ratio1_sigma_hn

sigma1 sigma2
-4e-04 -0.0972

ratio2_sigma_hn

sigma1 sigma2
1.1007 0.821

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
-0.0142 -0.1327

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.9657 0.8996

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.0076 -0.0897

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.9621 0.913

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0011 1.0009 1.0017 1.0009 1.0012 1.0012 1.0011
n.eff 8800.0000 11000.0000 2500.0000 11000.0000 5200.0000 5200.0000 7400.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 2.700e+05 5.400e+05 4.900e+05 4.500e+05 4.400e+05 3.600e+05 3.400e+05 
summary_print(N = 1000, J = 5)

4.2.4.2 J = 5

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
1841.19 38.91 93681.92 36.81
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.5351 0.0455 -1.5363 0.0457 -1.5346 0.0455 -1.5363 0.0457
beta12 2.0172 0.0430 2.0184 0.0434 2.0173 0.0430 2.0184 0.0434
beta13 0.9978 0.0460 0.9986 0.0474 0.9975 0.0460 0.9986 0.0474
beta14 -2.9929 0.0436 -2.9946 0.0437 -2.9932 0.0432 -2.9946 0.0437

ratio1_beta1_pc

-0.0376 0.0268 0.0236 -0.0323

ratio1_beta1_hn

-0.0373 0.0263 0.0235 -0.0324

ratio2_beta1_pc

1.0159 1.0553 1.0638 1.0275

ratio2_beta1_hn

1.0172 1.0344 1.0594 1.0102

ratio1_sigma_pc

sigma1 sigma2
-0.1576 -0.1273

ratio2_sigma_pc

sigma1 sigma2
0.5801 0.6254

ratio1_sigma_hn

sigma1 sigma2
-0.1769 -0.1686

ratio2_sigma_hn

sigma1 sigma2
0.5673 0.5666

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
-0.1459 -0.1147

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.8248 0.8557

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
-0.1715 -0.1606

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.8347 0.8307

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0009 1.0011 1.0009 1.001 1.0011 1.001 1.001
n.eff 11000.0000 10000.0000 11000.0000 11000.000 7400.0000 11000.000 11000.000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 5.400e+05 2.600e+05 5.400e+05 5.400e+05 5.400e+05 3.100e+05 2.700e+05 
summary_print(N = 1000, J = 10)

4.2.4.3 J = 10

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
1835.19 37.55 92609.21 36.08
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.5071 0.0446 -1.5109 0.0461 -1.5073 0.0447 -1.5109 0.0461
beta12 2.0590 0.0436 2.0611 0.0437 2.0587 0.0437 2.0611 0.0437
beta13 1.0171 0.0458 1.0184 0.0465 1.0170 0.0458 1.0183 0.0465
beta14 -3.0966 0.0431 -3.0984 0.0434 -3.0964 0.0429 -3.0984 0.0434

ratio1_beta1_pc

-0.0813 0.0543 0.0299 -0.0464

ratio1_beta1_hn

-0.0812 0.0544 0.0298 -0.0463

ratio2_beta1_pc

1.0728 1.0381 1.0282 1.0277

ratio2_beta1_hn

1.0732 1.0168 1.0313 1.0091

ratio1_sigma_pc

sigma1 sigma2
-0.0662 -0.0135

ratio2_sigma_pc

sigma1 sigma2
0.8348 0.8833

ratio1_sigma_hn

sigma1 sigma2
-0.0459 -0.0166

ratio2_sigma_hn

sigma1 sigma2
0.8509 0.8672

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
-0.0601 -0.0056

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.9315 0.9464

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
-0.0388 -0.007

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.9366 0.9316

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0009 1.0013 1.001 1.0009 1.0009 1.0012 1.0014
n.eff 11000.0000 4400.0000 11000.000 11000.0000 11000.0000 6800.0000 3900.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 1.100e+05 2.100e+05 4.100e+05 5.400e+05 5.400e+05 3.800e+05 5.400e+05 
summary_print(N = 1000, J = 25)

4.2.4.4 J = 25

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
1801.8 37.91 90073.21 42
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.5101 0.0442 -1.5164 0.0448 -1.5109 0.0439 -1.5164 0.0448
beta12 2.0039 0.0438 2.0071 0.0428 2.0038 0.0435 2.0072 0.0428
beta13 0.9910 0.0459 0.9974 0.0463 0.9915 0.0458 0.9974 0.0463
beta14 -3.0299 0.0431 -3.0335 0.0430 -3.0301 0.0431 -3.0335 0.0430

ratio1_beta1_pc

-0.1257 0.0778 0.1301 -0.08

ratio1_beta1_hn

-0.1258 0.0778 0.1301 -0.08

ratio2_beta1_pc

1.0502 1.0081 1.024 1.0034

ratio2_beta1_hn

1.0576 0.9804 1.0197 0.9738

ratio1_sigma_pc

sigma1 sigma2
-0.0224 -0.0136

ratio2_sigma_pc

sigma1 sigma2
0.9503 0.9515

ratio1_sigma_hn

sigma1 sigma2
-0.0174 -0.0031

ratio2_sigma_hn

sigma1 sigma2
0.9443 0.9597

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
-0.0209 -0.0114

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.9798 0.9752

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
-0.0151 -0.001

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.9709 0.9797

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0012 1.0017 1.0011 1.0009 1.0009 1.0018 1.0021
n.eff 6400.0000 2300.0000 6900.0000 11000.0000 11000.0000 2100.0000 1700.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001e+00
n.eff 5.400e+05 5.400e+05 5.400e+05 4.000e+05 5.400e+05 3.100e+05 1.900e+05 
summary_print(N = 1000, J = 1000)

4.2.4.5 J = 1000

Parameters Hyperparameters


times

JAGS dirinla pc LONG-JAGS dirinla hn
1900.09 42.22 94202.86 45.14
JAGS_mean JAGS_sd INLA_PC_mean INLA_PC_sd LONG_JAGS_mean LONG_JAGS_sd INLA_HN_mean INLA_HN_sd
beta11 -1.5240 0.0494 -1.5510 0.0455 -1.5239 0.0496 -1.5510 0.0454
beta12 1.9464 0.0492 1.9922 0.0438 1.9455 0.0486 1.9922 0.0438
beta13 0.9849 0.0492 0.9928 0.0461 0.9845 0.0495 0.9928 0.0461
beta14 -2.9883 0.0477 -3.0638 0.0438 -2.9884 0.0479 -3.0638 0.0437

ratio1_beta1_pc

-0.5465 0.9623 0.1674 -1.5717

ratio1_beta1_hn

-0.5464 0.9621 0.1675 -1.5716

ratio2_beta1_pc

0.8414 0.8324 0.8832 0.8317

ratio2_beta1_hn

0.8686 0.8152 0.8638 0.8161

ratio1_sigma_pc

sigma1 sigma2
0.7773 1.3511

ratio2_sigma_pc

sigma1 sigma2
0.9059 0.9123

ratio1_sigma_hn

sigma1 sigma2
0.7763 1.3439

ratio2_sigma_hn

sigma1 sigma2
0.9005 0.9126

ratio1_sigma_log_pc

log(sigma1) log(sigma2)
0.7618 1.2624

ratio2_sigma_log_pc

log(sigma1) log(sigma2)
0.8197 0.6906

ratio1_sigma_log_hn

log(sigma1) log(sigma2)
0.761 1.2561

ratio2_sigma_log_hn

log(sigma1) log(sigma2)
0.8147 0.6918

res_check_jags1

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.0009 1.001 1.0013 1.0012 1.0028 1.001 1.0069
n.eff 11000.0000 11000.000 5100.0000 6400.0000 1000.0000 11000.000 340.0000

res_check_jags2

beta1[1] beta1[2] beta1[3] beta1[4] deviance sigma1 sigma2
Rhat 1.001e+00 1.001e+00 1.001e+00 1.001e+00 1.001 1.001e+00 1.0011
n.eff 5.400e+05 5.400e+05 5.400e+05 5.400e+05 48000.000 2.500e+05 16000.0000